Answer to Question #293947 in Statistics and Probability for Nics

Question

It has been reported that the average credit card debt for college seniors is $3262. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds that the average debt is $2995, and the population standard deviation is $1100. Let’s conduct the test based on an alpha = 0.05.

Answer 1

We define the null hypothesis and alternative as below

H₀ : average debt =  $3262 ( null hypothesis)

H_{1 :}average debt < $3262 ( alternative hypothesis)

We then compute the z test defined as ( (2995 - 3262) / (1100/ 7.07) ) = -1.72

we obtain the critical value at 0.05 level of significance, with respect to a left tailed test = -1.645

From the above, out test value ( -1.72) is less than our critical value (-1.645) ,we therefore reject the null hypothesis.

Hence we may conclude that the student senate claim was right.